Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in PYTHON3):

Solution:

N = int(input())
a = [int(i) for i in input().split()]

a.sort()
a.reverse()


# i = 0, j = 1

ans = (a[2]+a[3]) / (a[0]-a[1])

# i = 0, j = 2

ans = max(ans, (a[1]+a[3]) / (a[0]-a[2]))


# i = 0, j >= 3

for j in range(3, N):
    ans = max(ans, (a[1]+a[2])/(a[0]-a[j]))

# i = 1, j = 2

ans = max(ans, (a[0]+a[3]) / (a[1]-a[2]))

# i = 1, j >= 3

for j in range(3, N):
    ans = max(ans, (a[0]+a[2])/(a[1]-a[j]))

# i >= 2

for i in range(2, N):
    for j in range(i+1, N):
        ans = max(ans, (a[0]+a[1])/(a[i]-a[j]))

print(ans)